The canonical equation of adaptive dynamics: a mathematical view

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On selection dynamics for continuous structured populations (2008, methodology): “If the stable strategy had always only one dominant trait, this procedure should lead to the canonical equation of adaptive dynamics as obtained in [3].”
A microscopic interpretation for adaptive dynamics trait substitution sequence models (2005, methodology): “The TSS model belongs to the recent biological theory of evolution called adaptive dynamics (Hofbauer and Sigmund, 1990; Marrow et al., 1992; Metz et al., 1992), and has been introduced by Metz et al. (1996) and Dieckmann and Law (1996) and mathematically studied in Champagnat et al. (2001).”
A beginners guide to adaptive dynamics (2002, background): “– AD as an added feature to a bifurcation diagram [20], – multi-dimensional traits, – when is mutation structure irrelevant for dynamics? [27, 60, 61], – co-evolution [22], – putting genetics underneath [21, 33, 35, 41, 50, 61, 27, 88], – does branching lead to speciation? [21, 33, 41], – bifurcatio”